So, in order to study the existence of invariant volume forms, for a Hamiltonian system on \(G/H\) , it seems reasonable to discuss the problem directly in the homogeneous Poisson space \(G/H\) . In fact, attempts to give a description of the modular class of the Poisson structure on \(G/H\)  has been given in [1]}, [2]}, and therefore, we could discuss the relation between the unimodularity of the Poisson structure and the existence of invariant volume forms for the Hamiltonian system.
